Buckling Instability in Growing Tumor Spheroids

Ciarletta, Pasquale

doi:10.1103/physrevlett.110.158102

Cited by 61 publications

(56 citation statements)

References 27 publications

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“…As an inherent limitation of our axisymmetric model, all our fold numbers are limited to even numbers. In agreement with the literature [32,33], we observe that the fold number increases with increasing radius-to-thickness ratio R/t: on a flat substrate, our analytical model indicates that the number of folds increases linearly with (R/t); on a spheroidal substrate, our computational model suggests that the mode number increases roughly proportional to (R/t) 5/8 . This value is lower than (R/t) and (R/t) 3/4 , the values reported for less curved flat and cylindrical substrates [34].…”

Section: Continuum Model Of Growing Bi-layered Systemsupporting

confidence: 88%

Size and curvature regulate pattern selection in the mammalian brain

Budday

Steinmann

Goriely

et al. 2015

Extreme Mechanics Letters

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Section: Continuum Model Of Growing Bi-layered Systemsupporting

confidence: 88%

Size and curvature regulate pattern selection in the mammalian brain

Budday

Steinmann

Goriely

et al. 2015

Extreme Mechanics Letters

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“…Most of them make use of the multiplicative decomposition of the deformation gradient tensor to account for tumor growth, evolution of growth-induced stress and/or the mechanical interactions with the surrounding normal tissue (2, 3, 51-54). Methodologies also exist that involve the incorporation of a growth strain factor to direct tumor expansion (28, 29).…”

Section: Solid Mechanics Of Tumorsmentioning

confidence: 99%

The Role of Mechanical Forces in Tumor Growth and Therapy

Jain

Martin

Stylianopoulos

2014

Annu. Rev. Biomed. Eng.

803

708

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Tumors generate physical forces during growth and progression. These physical forces are able to compress blood and lymphatic vessels, reducing perfusion rates and creating hypoxia. When exerted directly on cancer cells, they can increase their invasive and metastatic potential. Tumor vessels - while nourishing the tumor - are usually leaky and tortuous, which further decreases perfusion. Hypo-perfusion and hypoxia contribute to immune-evasion, promote malignant progression and metastasis, and reduce the efficacy of a number of therapies, including radiation. In parallel, vessel leakiness together with vessel compression cause a uniformly elevated interstitial fluid pressure that hinders delivery of blood-borne therapeutic agents, lowering the efficacy of chemo- and nano-therapies. In addition, shear stresses exerted by flowing blood and interstitial fluid modulate the behavior of cancer and a variety of host cells. Taming these physical forces can improve therapeutic outcomes in many cancers.

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“…The formation of stable folds in compressed thin films over soft substrates has been, instead, investigated by Brau et al (2011). In layered materials, the competition of the bulk energies has been also found to determine pattern selection and dynamics in many biological systems, from solid tumours (Ciarletta, 2013) to tubular tissues , in dependence of both size and elastic effects.…”

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confidence: 98%

Beading instability in soft cylindrical gels with capillary energy: Weakly non-linear analysis and numerical simulations

Taffetani

Ciarletta

2015

Journal of the Mechanics and Physics of Solids

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a b s t r a c tSoft cylindrical gels can develop a long-wavelength peristaltic pattern driven by a competition between surface tension and bulk elastic energy. In contrast to the RayleighPlateau instability for viscous fluids, the macroscopic shape in soft solids evolves toward a stable beading, which strongly differs from the buckling arising in compressed elastic cylinders.This work proposes a novel theoretical and numerical approach for studying the onset and the non-linear development of the elasto-capillary beading in soft cylinders, made of neo-Hookean hyperelastic material with capillary energy at the free surface, subjected to axial stretch. Both a theoretical study, deriving the linear and the weakly non-linear stability analyses for the problem, and numerical simulations, investigating the fully nonlinear evolution of the beaded morphology, are performed. The theoretical results prove that an axial elongation can not only favour the onset of beading, but also determine the nature of the elastic bifurcation. The fully non-linear phase diagrams of the beading are also derived from finite element numerical simulations, showing two peculiar morphological transitions when varying either the axial stretch or the material properties of the gel. Since the bifurcation is found to be subcritical for very slender cylinders, an imperfection sensitivity analysis is finally performed. In this case, it is shown that a surface sinusoidal imperfection can resonate with the corresponding marginally stable solution, thus selecting the emerging beading wavelength.In conclusion, the results of this study provide novel guidelines for controlling the beaded morphology in different experimental conditions, with important applications in micro-fabrication techniques, such as electrospun fibres.

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Buckling Instability in Growing Tumor Spheroids

Cited by 61 publications

References 27 publications

Size and curvature regulate pattern selection in the mammalian brain

Size and curvature regulate pattern selection in the mammalian brain

The Role of Mechanical Forces in Tumor Growth and Therapy

Beading instability in soft cylindrical gels with capillary energy: Weakly non-linear analysis and numerical simulations

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